topic: lumped integral Differential, formulation
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- This Problem Is For Course Lumped Integral Differential Topic Lumped Integral Differential Formulation Very Importa 1 (89.99 KiB) Viewed 15 times
- This Problem Is For Course Lumped Integral Differential Topic Lumped Integral Differential Formulation Very Importa 2 (136 KiB) Viewed 15 times
- This Problem Is For Course Lumped Integral Differential Topic Lumped Integral Differential Formulation Very Importa 3 (66.37 KiB) Viewed 15 times
- This Problem Is For Course Lumped Integral Differential Topic Lumped Integral Differential Formulation Very Importa 4 (57.48 KiB) Viewed 15 times
* The Care Pool reactor is made of cylinder fuel elements, each compouses of uranium rod of radis Randa Stainless Steel Cladding af negligible think ness (Fig 2-54) The are reactor has the suddenly to be generated in uranium rods us M 0² / 0 = 1- (1₁² where to is the internal energy generation at the center Line the temperture at The coolant in held constant at Too. The heat transfer coefficient is large, formulate the problem. *_attention to be formulated to under method. [INTEGRAL formulation
PROBLEMS |Coolant Steel cladding Scanned with CamScanner Uranium rod FIG. 2-54
Scanned with CamScanner EXAMPLE dedo del batten Tion 2-10. A Flat Plate of Think hess 22 having The uniform intial Temperature to is Plunged suddenly into a both at constant Temperature To (Fig 2-53) the heat transfer cae fcient is h the density heat capacity and thermal conductivity of The Plate are Sie and k, respectively formulated the Problem to be formulated to under method. attention. formulation INTEGRAL S h C k K2L To initial 2-53 temperature
ASSUMPTion: To > To LumPed E₁ E₂ dx Differential To(t) X Penetration de PTh L T'o h Scanned with CamScanner
INTegral formulation In-ouT+gen - Acc o-hA (T_T tozde dt O-KATI ax(x₂ Tott) +0₂05/ St [E₁ = Ser To 2 Sc (L- To (t) To A JE ₂2 Scdv Tz Sc Adx T-E2²J. SCATOX (+) dE (E+E₂) % -SCA- d 2 -SCA.T. To + df dt dt TJx It Initial conduction I.c Boundary conduction moT (ogt) 2 To & x 20 27 x₂ To(t) ~. +K=h(T₂-T) Temp Profile T_T = ax²²_ byte Boundary conduction. #B.c.2₂lax+b 29 (0) + b₂0_1620 #B.c.2→ T-Toz 9 (0)² + Caux Cro 2 B.clk (2ax) zh (Tx-ax-To) X₂% saz h(To-To) n To(hTo+2k) Temp Profile T-To ₂ h (TP-To) ² To (hTo+2k) 2 √ Tax=_h(T-- "T) T₂²_ + T. To 3(1To+2k) 2 d'To of Tdx₂h (To-To) J7 [3 (h To + 2k)] - 3hd10 h (To-To) T. ² d It JT q (1 To +2k)² 2 16x20 governing equution dTo что это dt (hTo+2k) dt + Scanned with CamScanner oft <tp Governing Equation ld dt sax 1x27 It Tax TodTo_KX₂T tzoT (₂0) z To Toz To (t)
Scanned with CamScanner X₂L> 9 -9 20 h (Tos-T)₂-(KT) dx LumPed. < Too To Governing Equation To L 2A(0)+B=0Bzo 1²_c_7₂) → C₂-A [ 2K² +²²] & ₂ h 1 M 2XL 3 A= → SJA = Sud T ১t In A+ Canszmt -> A= exp[mt-cons] #1.c temp Profile → T-To=A(3²-M) A (gtp) Consei z Mtp- - 2n Tx-T m T² Top ₂ exp[mt-cans ] (2²_m) t>tp In-our+genz Aсс ark A-oton КА ЭТ эт JE dt Seng Tax Id 1 Tax 2x Xel dt Ic tatp x₂0 ->T=To X₂0 T 20 B-c x=L - (- K²T ) = h (T_T) mK (ZAL)₂h (T-AL²³_c_ IXEL ax (x) O X -ml) To-T. m
Jo ni ih slet from A 6 Dow " (#) 41 40 an W open of het tansfer of 5.744 ( о тото на света. Similarly the Y-7₂-5 Boundary condition one 27-1₂7-50 Т.1-61-4.-9x) →0 то то-то су п 12 heat generated kin Cylindrical dement completely (Heat Conved at form kisface of you) my.0 h (го-то). To Ambient temperature •xt * Scanned with CamScanner рочLэш билом